would e5400 bottleneck hd 7770 ghz edition

Solution
Almost any CPU you can buy today will be more than twice as fast as your E5400 but will require a new motherboard and likely RAM to match. If you have an OEM Windows license, you will need a new license as well.

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Titan
Moderator
The old Core2Duo is nowhere near enough to get the most out of a HD7770.

I had an E8400 with an HD5770 and I could only push the GPU to 60-70% load in most games.

For modern games and more recent GPUs, you would want to aim for either a Pentium G3258 or i3-32xx.